Hierarchical analysis of large-scale control systems via vector simulation function

In this paper, we study the hierarchical problem of large-scale control systems. As a natural extension of traditional simulation function, the new notion of vector simulation function is introduced for investigating the hierarchies between abstract systems and concrete systems. By constructing a comparison system, we present a generalized result on this problem which, in the case of a scalar simulation function, specializes to the classical result. When interconnected nonlinear systems are considered, an easily checkable sufficient condition is obtained to facilitate the compositional construction of abstractions. Based on the condition, we propose a particular construction of abstractions for interconnected linear systems. Finally, two examples are included.